Euclidean

Examples of Euclidean in the following topics:

• Shape

  • In geometry, two subsets of a Euclidean space have the same shape if one can be transformed to the other by a combination of translations, rotations (together also called rigid transformations), and uniform scalings.
  • Having the same shape is an equivalence relation, and accordingly a precise mathematical definition of the notion of shape can be given as being an equivalence class of subsets of a Euclidean space having the same shape.

• Matrix and Vector Norms

  • For $p=2$ this is just the ordinary Euclidean norm: $\|\mathbf{x}\| _ 2 = \sqrt{\mathbf{x}^T \mathbf{x}}$ .

• Relativistic Energy and Mass

  • Here the term represents the square of the Euclidean norm (total vector length) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered.